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# High School Calculus Math Course Outline

## 1.0 Credit

This course includes a thorough study of differentiation and integration with many applications. Limits and continuity are investigated in-depth. The course will emphasize the importance of mathematics studied to date. After completion of this course, the student may wish to take the Advanced Placement Test.

1- Introduction & Review

- Welcome to Calculus
- Course Outline
- Course Syllabus
- Completing Math Assessments
- Calculus On The Web
- Review — Stuff You Should Already Know
- Pretest
- Assignment: Calculus Pretest

2- Limits & Continuity

- An Introduction to Limits & Continuity
- Quiz: Introduction to Limits & Continuity
- Tangent Lines & Rates of Change
- Handout: Tangent Lines & Rates of Change Worksheet
- Assignment: Tangent Lines & Rates of Change
- The Limit
- Handout: The Limit Worksheet
- Assignment: The Limit
- One-Sided Limits
- Handout: One-Sided Limits Worksheet
- Assignment: One-Sided Limits
- Computing Limits
- Handout: Computing Limits Worksheet
- Assignment: Computing Limits
- Infinite Limits
- Handout: Infinite Limits Worksheet
- Assignment: Infinite Limits
- Limits at Infinity
- Handout: Limits at Infinity Worksheet
- Assignment: Limits at Infinity
- Continuity
- Handout: Continuity Worksheet
- Assignment: Continuity
- Additional Resources
- Handout: Limits & Continuity Exam
- Assignment: Limits & Continuity Exam

3- Derivatives

- Introduction to Derivatives
- Definition & Interpretation of the Derivative
- Handout: Definition & Interpretation of the Derivative Worksheet
- Assignment: Definition & Interpretation of the Derivative
- Differentiation Formulas
- Handout: Differentiation Formulas Worksheet
- Assignment: Differentiation Formulas
- Product & Quotient Rule
- Handout: Product & Quotient Rule Worksheet
- Assignment: Product & Quotient Rule
- Derivatives of Trig Functions
- Handout: Derivatives of Trig Functions Worksheet
- Assignment: Derivatives of Trig Functions
- Derivatives of Exponential & Logarithm Functions
- Handout: Derivatives of Exponential & Logarithm Functions Worksheet
- Assignment: Derivatives of Exponential & Logarithm Functions
- The Chain Rule
- Handout: The Chain Rule Worksheet
- Assignment: The Chain Rule
- Implicit Differentiation
- Handout: Implicit Differentiation Worksheet
- Assignment: Implicit Differentiation
- Related Rates
- Handout: Related Rates Worksheet
- Assignment: Related Rates
- Higher Order Derivatives
- Handout: Higher Order Derivatives Worksheet
- Assignment: Higher Order Derivatives
- Additional Resources
- Handout: Derivatives Exam
- Assignment: Derivatives Exam

4- Applications of Derivatives

- What’s the Big Deal About Derivatives, Anyway?
- Rates of Change
- Critical Points & Extrema
- Handout: Critical Points & Extrema Worksheet
- Assignment: Critical Points & Extrema
- The Shape of a Graph
- Handout: The Shape of a Graph Worksheet
- Assignment: The Shape of a Graph
- The Mean Value Theorem
- Handout: The Mean Value Theorem Worksheet
- Assignment: The Mean Value Theorem
- Optimization
- Handout: Optimization Worksheet
- Assignment: Optimization
- Linear Approximations
- Handout: Linear Approximations Worksheet
- Assignment: Linear Approximations
- Midtest
- Assignment: Calculus Midtest
- Handout: Applications of Derivatives
- Assignment: Applications of Derivatives

5- Integrals

- Working Backwards
- Indefinite Integrals
- Handout: Indefinite Integrals Worksheet
- Assignment: Indefinite Integrals
- Computing Indefinite Integrals
- Handout: Computing Indefinite Integrals Worksheet
- Assignment: Computing Indefinite Integrals
- Substitution Rule for Indefinite Integrals
- Handout: Substitution Rule Worksheet
- Assignment: Substitution Rule
- Area Problem
- Handout: Area Problem Worksheet
- Assignment: Area Problem
- Definite Integrals
- Handout: Definite Integrals Worksheetv
- Assignment: Definite Integrals
- Computing Definite Integrals
- Handout: Computing Definite Integrals Worksheet
- Assignment: Computing Definite Integrals
- Substitution Rule for Definite Integrals
- Handout: Substitution Rule for Definite Integrals Worksheet
- Assignment: Substitution Rule for Definite Integrals
- Integration by Parts
- Handout: Integration by Parts Worksheet
- Assignment: Integration by Parts
- Partial Fractions
- Handout: Partial Fractions Worksheet
- Assignment: Partial Fractions
- Improper Integrals
- Handout: Improper Integrals Worksheet
- Assignment: Improper Integrals
- Additional Resources
- Handout: Integrals Exam
- Assignment: Integrals

6- Applications of Integrals

- What’s the Big Deal About Integrals, Anyway?
- Area Between Curves
- Handout: Area Between Curves Worksheet
- Assignment: Area Between Curves
- Volumes of Solids of Revolution (Part 1)
- Handout: Method of Rings Worksheet
- Assignment: Method of Rings
- Volumes of Solids of Revolution (Part 2)
- Handout: Method of Cylinders Worksheet
- Assignment: Method of Cylinders
- Volume
- Work
- Handout: Work Worksheet
- Assignment: Work
- Assignment: Applications of Integrals

7- Sequences & Series

- Sequences & Series
- Sequences
- Series: The Basics
- Series: Convergence & Divergence
- Special Series
- Integral Test
- Comparison Test
- Alternating Series Test
- Absolute Convergence
- Ratio & Root Tests
- Strategy for Series
- Estimating the Value of a Series
- Power Series
- Taylor Series
- Additional Resources
- Post-Test
- Assignment: Sequences & Series

8- Course Survey

- Handout: Course Survey
- Assignment: Course Survey

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